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Hence disk 0 is the smallest one, and disk h − 1 the largest one. The following is a procedure for moving a tower of h disks from a peg A onto a peg C, with B being the remaining third peg: If h > 1, then first use this procedure to move the h − 1 smaller disks from peg A to peg B. Now the largest disk, i.e. disk h can be moved from peg A ...
The problem concerns two envelopes, each containing an unknown amount of money. The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for the Bayesian interpretation of probability theory. It is a variant of an older problem known as the necktie paradox.
The competitors had to pick out the six prettiest faces from 100 photos, and the winner is the competitor whose choices best matches the average preferences of all the competitors. Keynes observed that "It is not a case of choosing those that, to the best of one’s judgment, are really the prettiest, nor even those that average opinion ...
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The algorithm Basile created generates a 'book' by iterating every permutation of 29 characters: the 26 English letters, space, comma, and period. [8] Each book is marked by a coordinate, corresponding to its place on the hexagonal library (hexagon name, wall number, shelf number, and book name) so that every book can be found at the same place every time.
100 prisoners problem. Each prisoner has to find their own number in one of 100 drawers, but may open only 50 of the drawers. The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive.
A probabilistic generalization of the pigeonhole principle states that if n pigeons are randomly put into m pigeonholes with uniform probability 1/m, then at least one pigeonhole will hold more than one pigeon with probability. where (m)n is the falling factorial m(m − 1) (m − 2)... (m − n + 1). For n = 0 and for n = 1 (and m > 0), that ...
Buffon's needle was the earliest problem in geometric probability to be solved; [2] it can be solved using integral geometry. The solution for the sought probability p, in the case where the needle length l is not greater than the width t of the strips, is. This can be used to design a Monte Carlo method for approximating the number π ...